The SSTs fill a niche role in the aviation industry, flying people across oceans in a few hours. They can be operated with a small profit margin, but at the correct timing. Even if the Concorde flights had not been discontinued in 2003, they would eventually be hammered by the oil prices, because other aircraft can be rerouted, the fare policies changed, and a host of other tricks can be performed by airlines to minimize damages.
But an SST is a high cost, high maintenance, low profit business, since its passenger target group is so small that it cannot guarantee a minimum and stable income for the airline, especially when it is almost impossible to offer both Mach speeds and Jumbo ranges. In view of this, the SST seems altogether a bad idea, if you also take into account that the Internet has made the world a smaller place in many ways.
Most business can be now conducted without crossing the Atlantic, and airfares are becoming cheaper by using more efficient engines and aircraft designs. An SST right now would not be an exciting new supersonic way to fly, but a retro oddity. Still, the idea is being tossed around from time to time by various companies and agencies, re-emerging in various forms.